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sum of determinants

Source: 2017 South Korea USCM P1

August 15, 2020
linear algebramatrixDeterminantsSummationcollege contests

Problem Statement

n(≥2)n(\geq 2) is a given integer and TT is set of all n×nn\times n matrices whose entries are elements of the set S={1,⋯ ,2017}S=\{1,\cdots,2017\}. Evaluate the following value. ∑A∈Tdet(A)\sum_{A\in T} \text{det}(A)
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